LIBRARY OF CONGRESS 




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Kahn System of 
Reinforced Concrete 




Perspective of general adaptation. 



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Trussed Concrete Steel Co., 

Union Trust Building 
Detroit, = ; Michigan. 



LIBRARY of CONGRESS 
Two Copies Received 
JUN 20 1904 
Q Copyright Entry 

•CLASS CL-XXc. No! 



TA&S3 
T*7 



04-/W? 



HOME OFFICE 

UNION TRUST BUILDING, 

DETROIT, MICHIGAN. 






Representatives: 



V 



NEW YORK, N. Y. 

TRUSSED CONCRETE STEEL CO., 

160 FIFTH AVE. 



CHICAGO, ILL. 

KNAPP BROS., 

123 FRANKLIN ST. 



BALTIMORE, MD. 

TRUSSED CONCRETE STEEL CO., 

LAYTON F. SMITH, 

612 NORTH CALVERT ST. 



MILWAUKEE, WIS. 

NEWTON ENGINEERING CO., 

42 HATHAWAY BLDG. 



BUFFALO, N.Y. 

EASTERN CONCRETE STEEL CO., 

400 D. S. MORGAN BLDG. 



LOUISVILLE, KY. 

NATIONAL CONCRETE CONST. CO., 

140 W. MAIN ST. 



CLEVELAND, OHIO. 

JULIUS TUTEUR, 

529 WILLIAMSON BLDG. 

TORONTO, ONT. 

ALFRED J. STEVENS, 

49 CANADA PERMANENT BLDG. 



ST. LOUIS, MO. 

TRUSSED CONCRETE STEEL CO., 

J. P. ANNAN, 

CHEMICAL BLDG. 

PITTSBURG, PA. 

TRUSSED CONCRETE STEEL CO., 

FARMERS' BANK BLDG. 



SUPPLEE ENGINEERING CO., 
ERIE. PA. 



STEEL WORKS AT DETROIT AND PITTSBURG. 
TILE WORKS AT AKRON, OHIO. 





CROSS SECTION OF BAR. 




The Kahn Trussed Bar* 



Note. — This handbook is revised in accordance with the most 
recent practice of the Trussed Concrete Steel Co., and should be 
given preference to all previous issues. 




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Kahn System of Reinforced Concrete 



So much actual work is being done at the present time with reinforced 
concrete, and in general, the subject is receiving such intense interest by those 
taking part in buildings, bridges, or other constructions, that the new method 
of steel reinforcement herein described, it is believed, will be of interest. 

The advantages of reinforced concrete above steel, masonry, or wood, are 
so well known, that it is hardly necessary to enter into comparison here. Rein- 
forced concrete is absolutely free of any of the serious objections which exist 
in the use of these other materials. It is fire proof, and rust proof, but what is 
most advantageous about this type of construction, is the fact that its strength 
continually increases with age. 

Reinforced concrete lends itself admirably to the construction of walls, 
columns, floors, roofs, and all parts of buildings; to bridges, arches, culverts, 
abutments, retaining walls, tunnels, foundations, railway ties, and in general, 
it replaces, to advantage, all masonry or steel construction. 

The Kahn trussed bar consists of a half truss, struck up directly from a 
single rolled section, and provides the tensional members only. Concrete 
within itself is an excellent material to take up compressive strains, but is com- 
paratively weak for resisting tensile strains. The Kahn bar, when imbedded 
in a mass of concrete, therefore, supplies strength to the latter where this is 



J7 



lines , of pnncipa/ compressive s/ress . 




Fid.l.. Showing lines of principal 
stress in a unifbrm/y loaded beam 
^uppor-red ar ends . 



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most necessary, and the combination of the two materials, forms a complete 
truss. The main virtue of this trussed bar lies in the fact that concrete is 
reinforced wherever it is deemed necessary, that the steel extends upwardly 
into the mass, as well as lying merely along its bottom edge. This, then, in 
short, is the essence of this new type of construction, and a further reading 
of this pamphlet will show the large number of its applications. 

It is fairly well recognized among engineers, that vertical reinforcement 
for concrete beams is just as essential as the horizontal reinforcement, and in 
many cases to accomplish this purpose, the horizontal rods are surrounded by 
U shaped stirrups of band or twisted iron. It was noticed at first by European 
engineers that a concrete beam, when tested to destruction under uniform 
loading, invariably failed by shear at the ends, the lines of rupture correspond- 
ing closely to the lines of principal compressive stress for such a beam, as is 
shown in Figure 1. In this country engineers were apparently very slow to 



Kahn System of 



realize the importance of such vertical reinforcement. In fact, upon its strong 
recommendation by one of the U. S. Engineer Corps in a leading Engineering 
Journal, a number of engineers argued the matter strongly and pointed out 
tests which they had actually made, where apparently the break did not occur 
at the ends of the beam. Without one exception, however, these tests, when 
investigated, proved to be beams which had been loaded either unfairly, so as 
not to develop strains actually occurring in building practice, or they referred 
to beams so abnormally proportioned that they could not possibly be used. 

The Trussed Concrete Steel Company has made a number of tests on 
beams reinforced with plain and deformed rods on the bottom, and without 
one exception, all such beams, when tested to destruction under uniform load- 
ing, failed suddenly by vertical cracking or shear through the concrete, or 
longitudinal shear along the end o<f the rod. 

This matter of vertical reinforcement is certainly of more importance than 
some American Engineers have been willing to grant. It seems most natural 





Fig. 2. 



that rupture should occur in this manner. In fact, one can hardly conceive of 
its occurring in any other way. It must, of course, be remembered that a 
beam, when tested for both shear and bending moment, should be subjected to 
a uniformly distributed load, not to a concentrated center load: for, a beam 
loaded according to this latter method would only develop one-half the shear 
which exists in a uniformly loaded beam for a given bending moment. 

Take, for example, a certain beam, as shown in Figure 1, and consider the 
cross section' "AA." 

The tension strain on each fibre below the neutral axis, varies in propor- 
tion to its distance therefrom. The vertical shearing is, however, practically 
constant. The resultant strain on any particle should therefore be a combina- 
tion of these two components, producing a line of principal tensile stress, which 
is one of variable curvature from the bottom of the beam to the top. 



Reinforced Concrete 



If, then, lines of principal tensile stress exist throughout a beam, it is most 
natural that the concrete, being weak in tension, should open at right angles 
to these lines, and this is what has occurred in all the tests which me writer has 
observed in well proportioned concrete steel beams, when tested ro destruction 
under uniform load, and where the metal reinforcement was horizontal only. 

As has already been noted, European engineers endeavored to overcome 
the difficulty by placing stirrups throughout the beam, their distances apart 
varying, of course, in the inverse ratio of the shear. There seems no doubt 
whatever in the writer's mind that such stirrups accomplish a great deal of 
good, as they cross the lines of rupture at an angle, and tend to hold the material 
together. If, however, they are placed in a beam, they should be placed in a 





Diacjbam • vShowimq .Thctss Action- 




'Dt^qR^M Showinq PlatArch AcnoM 



Fig. 3. 



direction inclined to the horizontal, so as to lie more closely along the line of 
principal tensile stress, for if they lie in exactly this line, they also cut the 
actual line of rupture at right angles, and are therefore of maximum efficiency 
in holding together the concrete where its natural tendency is to open up. 
Furthermore, if such stirrups are to carry stress, they should carry it into 
some member capable of receiving it, and the bottom chord member or the 
horizontal reinforcement is there for that purpose. In the first place, then, it 
seems to the writer that stirrups should be inclined to the vertical and prefer- 
ably bent to a curvature to approximate the line of principal tensile stress, 
and secondly, these stirrups should be rigidly connected to the main horizontal 
reinforcing bar. 

There is still another matter in connection with the steel reinforcement 
for concrete beams, which is also of great importance, in so far mat it affects 
economy in the use of steel. In a uniformly loaded beam, the maximum bend- 



10 



Kahn System of 



i.ng moment occurs at the center, whereas the maximum shear occurs at the 
ends, and if the same quantity of steel reinforcement is therefore placed along 
the bottom of the beam and extends the full length of it, it does seem to 
the writer that steel has been wasted so far as bending moment alone is con- 
cerned, and certainly the beam has been neglected so far as shear is con- 
cerned. A steel I beam in this manner is not an economical construction for 
uniform loading; its top and bottom flanges are only required at the center 
and at this place only a very thin web, whereas at the ends the stress is almost 
altogether shear, and web alone is required with very little of top and bottom 
flanges. 

In the system of concrete reinforcement, which it is the purpose of this 
pamphlet to describe, these two matters have been carefully considered. The 
fundamental principles of this type of reinforcement are : 

1st. Concrete should be reinforced in a vertical plane, as well as in a 
horizontal one. 

2nd. The reinforcement should be inclined to the vertical preferably 
with varying upward curvature, approximating the line of principal tensile 

stress. 

3rd. The metal should be distributed in proportion to the strains existing 
at any place. 

-1th. The shear members should be rigidly connected to the horizontal 
reinforcement steel. 

It has been endeavored to accomplish all of these results by taking a 
bar of cross section, as shown in Figure 2, and shearing upwards into an 
inclined position the web on both sides of the main body, thereby forming 
substantially the tension members of the ordinary Pratt Truss. When such 
a structural member is embedded within a body of concrete, the latter unites 
firmly to the steel, and the combination of the two forms a trussed beam 
wherein the tensional members are made up of steel, and the missing com- 
pression members supplanted by the concrete. Concrete is. excellent in com-" 
pression; steel, in tension; and, thanks to the property of strong adhesion 
between the two, in their combination is made a most ideal beam. 

Neglecting for a moment the matter of vertical reinforcement, it is very 
evident that a bar sheared up as above described, can not possibly slip through 
the concrete. The writer has actually taken blocks of concrete, moulded to 
form the voussoirs of a flat arch, and then set them between the prongs. Such 
a beam, though set up without a particle of mortar between the joints, will 
carry a very heavy weight, and were it not for the large defleccion which is 
caused by the poorly fitting surfaces between the prongs and blocks, such a 
beam would carry weights to the same extent and on the same principle 
as when steel and concrete are actually united together. 

And this presents another way of looking at the reasons why this method 
of reinforcement is so efficient. As soon as a load is applied on top of the 



Reinforced Concrete 



11 



beam, the concrete tends to arch itself, and a series of internal arches immedi- 
ately set themselves up within the material, each arch finding its abutment in a 
set of prongs for which the bottom chord acts as a tie. The prongs receive 
the weight and carry it upwards, distributing it on the other arches of larger 
span, the horizontal reinforcement serving as a common tensional member. It 
is plainly evident that with this construction the horizontal member might actu- 
ally be placed entirely outside of the concrete, and the adhesion of the concrete 
to it entirely neglected, the strains coming into it being so largely the horizontal 
components of the inclined members. Of course, for fire proofing purposes, 
and to prevent rusting, it is more advisable to imbed the steel within the con- 
crete, and when this is done, advantage may be taken of both the adhesion of 
the concrete to the main bar and to the sheared up members. In fact, with a 
given amount of concrete, a maximum amount of steel may be used, since the 
strains which it takes up are due to the direct adhesion of the concrete to it. plus 
the horizontal component of the inclined members. When such a beam fails, 
assuming that good material has been used for its construction, one of two 
things must happen, — either the steel pull in two, or the concrete crush on top. 
The top portion of a concrete beam when used in floor construction, is largely 
the floor itself, and it is generally impossible for this to fail in compression. It 
would seem, therefore, that a very large quantity of steel could be placed in the 
bottom of the beam to balance the compression. In fact, in all tests which the 
writer has made up to date, he has pulled the steel in two at the center of 
the beam. 




PERSPECTIVE VIEW OF SHEARED. BAR 





















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DIAGRAM SHOWING TRUSS ACTION 



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BARS AS USED IN BEAM AND FLOOR CONSTRUCTION 



Fig. 3a. 



Another point of great advantage of this construction is the fact that a beam 
need not necessarily be very wide to carry a given load ; depth alone counts to 
advantage. The steel reinforcement, depending entirely upon the stresses com- 
ing into it from the sheared up members, may be one large bar. This is prac- 
tically impossible with constructions wherein the stresses coming into the steel 
are due to adhesion only of the concrete to it. Where such adhesion is de- 
pended upon, a large bod)' of concrete must surround the steel to be able to 



12 



Kahn System of 



transmit all of the strain which the bar is capable of taking. Whatever strain 
exists in the steel must be transmitted into the upper portion of the concrete 
immediately surrounding it, and any one can readily perceive the enormity of 
the horizontal shear, which must therefore exist throughout the body of the 
concrete, and the necessity of giving this great width. With this new method 
of concrete reinforcement, however, the beam may be comparatively narrow; 
in fact, at the bottom it needs only to be sufficiently wide to encase the steel. 
It should taper upwards, however, widening towards the top, so that sufficient 
area may be given to the concrete to receive the compression. This, of course, 
makes a remarkable saving in the amount of this material used. 

The strength of steel is, of course, a definitely determined matter. As for 
the concrete, it is not very expensive, and it would be advisable in all cases to 
give a small surplus of this material on the top of a beam, so that it will not 
fail by compression. With shear thus properly cared for, there is only one 
way in which the beam can possibly fail, and that is by the parting of the 
steel. Where this result can be assured with certainty, a concrete beam need 
no longer be subjected to a factor of safety of "ten" : the ordinarily adopted 
factor of T "four" is sufficient, as such a beam is entirely dependent upon the 
steel and should be subject to close calculation in the same manner as a steel 
I beam or truss. When a concrete beam fails by shear, as has occurred almost 
without exception in tests up to date, then indeed, the engineer stands more 
or less in mystery. In general it seems to the writer that whenever concrete is 
depended upon to carry other strains than direct compression, more or less 
risk is being assumed by the designing engineer, and a large factor of safety 
is strongly recommended. 

Some photographs are submitted herewith of tests made on t^vo reinforced 
concrete beams, of twenty-six feet span, center to center of supports, with a 
four-inch thick concrete slab five feet wide on top to receive the load. The 
concrete was made of Portland cement, sand, and crushed stone, proportioned 
one, two and five. Loading was done with pig iron. Deflections measured at 
the center. In one of the photographs, an outline is shown of the actual cross 
sections of the beams. The ends, it will be noted, are built up solid to give 
better bearing on the supporting timbers. The area of metal ^'n the bottom 
of each beam was two square inches. No deflection whatever could be observed 
in the beams until the load had reached 48,000 pounds. When 84,000 pounds 
of pig iron had been loaded on the beams, making a total weight of 93,000 
pounds thereon, the floor slab, weighing about 9,000 pounds, the^actual deflec- 
tion was five-eighths of an inch. It was evident that the elastic limit of the 
steel had been well exceeded by this time. With 101,100 pounds of pig iron, 
plus 9,300 pounds for weight of slab, making a total load of 110,400 pounds', 
the beam failed, breaking at the center, and pulling the steel in two at this 
point. Not a sign of a crack was to be seen throughout the beam at any other 
place than at the point of failure. This seems to the writer a very remarkable 
test. The absolute lack of even a hair-like crack throughout any portion of 
the beam, except at the place of failure, is clear evidence that shear was prop- 
erly provided for. 



Reinforced Concrete 



13 



torcement, the 

adhesion of the concrete to the horizontal steel member is not essential ; in 
fact, if the latter were placed entirely outside of the concrete, the beam would 
be very nearly as efficient, as the strain which comes into this lower chord is 
so largely the summation of the horizontal components of the inclined mem- 
bers. 

This principle is utilized in the Kahn patented trussed lintel, drawings and 
photographs of which are presented herewith. In the old system of lintels, an 
I beam or built-up girder was figured on to carry the weight of the superim- 
posed load and a 12xj4 inch or other similar plate was riveted to the bottom 
flanges of the beam to give bearing for the wall above, but the plate was 
counted upon as rendering little or no service in strengthening the lintel. In 
the new system this bearing plate not only supports the brick-work directly, 
but also acts as the bottom flange of a masonry beam, in which the masonry 
takes up the compression or thrust of a flat arch, while the steel plate takes up 
the tension.. Diagonals, riveted to the base plate, form abutments for a series 
of arches of stress, which set themselves up within the masonry, and for these 
the base plate serves as the bottom chord or tie. Each diagonal carries its 
weight upwards on the principle of the ordinary truss and spreads it on other 
arches of larger span, each of which has its corresponding abutment in a set 
of diagonals. 

Another way of looking at the steel reinforcement for such a masonry 
beam, is to regard it as a half truss, made up of tension members only, the 
masonry supplying the missing compression members, and the two being 
firmly united to each other through the cement, which forms a perfect bond 
between them. 

One of the photographs submitted herewith shows such a lintel, consist- 
ing of a 12"x;!4" steel plate, to which l"x}4" diagonal members were 
riveted. The span was twelve feet, height of lintel eleven inches, breadth thir- 
teen inches. Steel billets weighing 110 to 170 pounds were loaded on the beam 
until a total weight of 40,720 pounds was reached, equal to 3,400 pounds per 
linear foot of beam. The deflection was J4 inch. Loading was stopped at this 
point, as the beam was beginning to be very top heavy, and it was feared 
might turn over and injure the workmen. 

The above systems of concrete reinforcement which have been described 
are controlled by patents granted and now pending, which are held by the 
Trussed Concrete Steel Company, Union Trust Building, Detroit, Mich. 



14 



Kahn System of 







Fig. 4. 

Showing method of failure for concrete, reinforced in accordance with old systems, 

using twisted rods. Span 18 feet. 



Figures 4, 5, and 6, show tests made at Washington by the United States 
Engineers, on reinforced concrete beams and slabs, wherein twisted steel rods 
had been placed along the bottom of the floor. The methods of failure and 
reasons for it will at once become apparent to the engineer or architect. No 
matter how much horizontal reinforcement might have been placed in these 
floors, their strength would not have been increased. The probability is that 
their strength would have been greatly decreased, as the multiplicity of rods 



Reinforced Concrete 



15 



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Fig. 5. 
Failure of concrete by shear, reinforcement horizontal only, using deformed rods. 



would only have cut up the concrete at the bottom, wherein the enormous shear- 
ing strain existed, to which attention has already been called. The floors 
failed by longitudinal shear along the ends of the rods where this is maxi- 
mum. All the twisting in the world would not have prevented it, nor 
would this twisting, to the slightest extent, have decreased the vertical 
shear, which, it is very apparent, was fundamental in the cause of failure. 
It is unscientific to neglect this matter of shear, and to imagine that concrete 



16 



Kahn System of 




Fig. 6. 



Note failure of concrete when horizontal reinforcement only is used, 
failure correspond to lines of principal compressive stress. 



Lines of 



within itself is capable of taking this strain. Tests for shear have developed 
strengths remarkably low. The writer has never been able to secure results 
of more than 200 to 400 lbs. per square inch. Why, therefore assume such 
risk in reinforced concrete? There is only one way to prevent failures such as 
have been shown in these photographs, and that is by strengthening the floors 
both longitudinally and horizontally for shear, as well as bending moment ; 
and this, it is believed, has been well accomplished by the Kahn system of 
Trussed Reinforcement. 



Reinforced Concrete 



17 




Fig. 7 



Beams reinforced with Kahn System. Span 26 feet. Load, pig iron. 



Figure 7, 8, 9 and 10 show tests of the same nature., made on two beams 
strengthened in accordance with the Kahn system of reinforcement These 
beams were 20 feet span. Please note the comparison of loadings between 
them and the floors of 18 feet span with twisted rods. When failure occurred 
in these beams, the rupture was absolutely central. The steel pulled in lwo. 
Not a sign of a crack was to be observed throughout the beam at any other 
point. Maximum efficiency was, therefore, given to the strength of the beam. 
The accomplishing of this result is of especial interest to the engineer, from 
the fact that he can design with certainty. If the steel pulls in two, he can 
calculate the strength of the concrete beam with the same accuracy as the steel 
I beam. Even more so; for the I beam, under test to ultimate destruction, will 
buckle in its top flange long before the bottom flange pulls in two. 



Kahn System of 




Fig. 8. 
Two beams reinforced with Kahn System. Span 26 feet. 



Reinforced Concrete 



19 




Fig. 9. 



Load 84000 lbs. pig iron on two Kahn reinforced beams. Compare these with 

Fig. 6 where span is only 18 feet. 



20 



Kahn System of 




Fig. 10. 



Failure of two Kahn reinforced beams 

Load : Pig iron 101100 lbs. 

Weight of floor slab 9300 lbs. 



Total weight on beams 110400 lbs. 
Beam failed in center pulling four bars of steel in two. Compare with Fig. 6. 



Reinforced Concrete 



21 




Fig. 11. 



Figure 11 shows the Kahn patented Trussed Bar. It is very interesting 
to note how readily it adapts itself to all types of construction. Its application 
to columns, walls, latticed girders and trusses is fully as simple as its applica- 
tion to beams. Where a column is to be constructed, the bars are set in the 
corners of the concrete, and the shear members extend across the body, form- 
ing practically a latticed column. The reasons for the efficiency of such a 
column will be very apparent. Under ordinary circumstances, a steel bar is 
steadied at points very closely together, then the entire strength of the steel 
can practically be developed. This result is accomplished hi the steel rein- 
forcement of a column, clue to the hold of the concrete on the prongs. Fur- 
thermore, when the concrete tends to buckle, the steel comes into play on the 
principle of the ordinary latticed girder. In other words, the steel and con- 
crete mutually reinforce each other. 

Where moving loads are to be taken into account, it is best to place Kahn 
Trussed Bars in both the bottom and top of the beams, thereby producing 
practically a latticed girder. 



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Lines of rupture 



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nahn method of providing for- shear 



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Kahn affernaiive method of re/'nforce men/ 
for moWff<£ /ood. 

Fig. 12. 



22 



Kahn System of 



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/#*?". Area .36" "Weight JA^perft. 



These bars can have 
any standard size cuts as 
shown in Figure 14 and 
will be sent in lengths as 
ordered. In making cal- 
culations for strength of 
reinforced beam, assume 
the area of the entire 
cross section as here 
given. 




^J " * i '. Area ™ ' " Weight 2. 7* per ft. 




3"*r. Area IAZ ' " Weight 4.8* per ft. 




I'lG. 13. 



-3>£ x li". Area 2.0° " Weight 6.9 *per ft. 



Reinforced Concrete 



23 








%' 6- ffi 6' $" 6' $f 6 



6" %<' 6' 9 A\ 6" £»* 6 



ti" cuts for ^"xl%" bars 





E 



8" and 12" cuts for %" x 2 X \" bars 




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18" and 24" cuts for Ii4"x3%" bars 



Bars kept in stock ready for immediate delivery, in any lengths with standard cuts. 

Fig. 14. 



Figure 13 shows standard sections of the Kahn Trussed Bars. Practically 
any construction can be built by using one of the four sizes shown and sheared 
up as is indicated in Figure 14. The equivalent of Steel Beams from 6 inches 
to 20 inches can be built up with reinforced concrete, using one or more of 
these bars placed in the bottom, or on the tension side. 



Figure 14 shows standard cuts. It will be noticed that the largest is IS 
inches. Where deeper girders are wanted, it will be well to lay some of the 
rods horizontally all the way along the bottom, and others slanting upwards 
from the bottom towards the ends of the beam, thereby distributing the shear 
members throughout the beam, and causing them to reach its very top. 



24 



Kahn System of 







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Reinforced Concrete 



25 




Test load on floor reinforced with ^4 in. x 2^4 in. Kahn Trussed Bars. Span 16 ft, thickness of slab 
6 inches, bars 14 in. on centers. Total load 26 tons, equals 850 lbs. per square foot. 
No deflection. Floor intended to carry safe load of 125 lbs. per square foot. 



26 



TOP REINFORCING BARS- 



^—TO P REINFORCING BAKZ> ~^r~-^ , I 



Section "a." 



7o/=> KE/Mrorrc/AJG Satts, 




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Plan 

Fig. 15. 

Note. — For extra heavy beams place one or two short bars in girder as shown 
in Section " a." 



27 



Tables giving sizes and reinforcement for square 

panels, according to the Kahn System 

of Reinforced Concrete 



Type I 

Panel 16' x 16 7 between Supports 



ve 
per 
e foot 




Beam A 




Beam B 




Floor Slab 


OS 




Safe Li 
Load 
squar 


b 














Pounds 
Steel 
sq. ft. 


Cubic f 
Conci 

per sq 


d 


Steel 


b 
10 


d 
13 


Steel 


t 


s 


Steel 


J75 


12 


20 


2— H"x3f" 


2— l"x3" 


4" 


16" 


Y'*W 


3.60 


0.48 


200 


12 


22 


2— H"x3f" 


10 


14 


2— l"x3" 


4" 


16" 


Y'xW 


3.60 


0.50 


225 


12 


24 


2— i|"x3f" 


10 


16 


2— l"x3" 


4" 


16" 


V'xH" 


3.60 


0.53 


250 


16 


18 


3— H"x3f" 


10 


18 


2— l"x3" 


4 // 


14" 


Y'xW 


4.17 


0.53 


300 


16 


22 


3—H"x3f" 


10 


20 


2_ l"x3" 


4 // 


12" 


2 XJ 5 


4.37 


0.58 


350 


16 


24 


3— l|"x3f" 


10 


24 


2— l"x3" 


4// 


10" 


5 AX 2 


4.65 


0.62 



Panel 18 / xl8 / between Supports 



Safe Live 
Load per 
square foot 


Beam A 


Beam B 


Floor Slab 


Pounds of 
Steel per 
sq. ft. 


Cubic feet of 
Concrete 
per sq. ft. 


b 


d 


Steel 


b 


d 


Steel 


t 


s 


Steel 


J50 


12 


24 


9 1 1// V Q3// 

O J. 4 2L O 4 


10 


16 


2—1" x3" 


4" 


16" 


i// T i i// 

2 Xli) 


3.26 


0.50 


J 75 


12 


28 


2— l£"x3f" 


10 


18 


2—1" x3" 


4" 


16" 


¥'*W 


3.26 


0.54 


200 


16 


21 


3-li"x3|" 


10 


20 


2—1" x3" 


4" 


14" 


Y'xiY' 


3.80 


0.55 


225 


16 


24 


3-H"x3f" 


10 


22 


2—1" x3" 


4" 


12" 


Y'*W 


4.00 


0.58 


250 


16 


26 


3— U"x3f" 


12 


18 


9 1 l^vQ3// 
— J 4 AO4 


4" 


11" 


1// 1 1// 


4.59 


0.58 


300 


16 
20 


30 
23 


3— li"x3f" 
4— H"x3|" 


12 


22 


2-l 4 -"x3f" 


4" 


9" 


1// V 1 1// 

2 xl 2 


4.93 
5.31 


0.64 
0.63 



m r> • t - t> f In Slab over Beams, 3 Bars, i"xl£" x4'0" long 
Top Reinforcing Bars (« Beams " Supports, 5 » f"x2&"x8'0" " 



See Fig. 15. 



28 



II 



-TOP REINFORCING BARS 



.b_ 



Section "a." 



TOP KUNf-U KLINU DMrto- ■ ; i ^figugn « «■ iw---v l ; ll Vr ■-.■■-- 1 *> 



^*>- 




Plan. 

Fig. 16. 

Note. — For extra heavy beams place one or two short bars in girder as shown 
in Section "a," 



0) 



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fl. 


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Pounds of 
steel per sq. ft. 


M 


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CM CO CM CM CO CO . 


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CM "* CO CO ^ 
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Floor Slab 


Trus . 
Con. 
Bars 


rHfc^ HCN iHJNHNiHIN 


CO 


CM © OO It- CO 

rH rH 


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43 

co 


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CM 00 CM 00 CO OO 

y y y y y y 

cc]^ ccH 

H i— f i-H i— 1 

1 1 1 1 II 
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CM r-1 CM i-H CM CM 




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GO O CO O O O 

l—l 1— ( 1— 1 T— 1 


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a 

CD 

pq 


i—l 

CD 
CD 

CO 


co co oo co co 

ri rH i^S rS *^S 
CO CO CO Tf -^ 


TJ 


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CM CM CM CM CM 


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CO CO CO o o 

t— ■ i—l i-H CO CM 


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9 ATT e .f B S 


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^ *-> *a ^.(M 



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9^9.I0UOQ 

jo 1J99J oiqno 


cC 00 O CO N CO 
lO O CO CO C N 

o o o o o o 


Pounds of 

steel per sq. ft. 




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CO CO Ttf "^ TJH -^ 

CM CM CO CO CO CO 


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CM ^ CO CO 00 ^ 

CC OJ r-i Tl" N CM 

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Trus. 
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co' 


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5 


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CD 

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CO CM CO CO CO CO 

y y y y y y 

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i— 1 CM i— 1 rH ^H Ol 


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CO CO O O O O 
i— i i— ( r— 1 i— i 


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CD 

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r— i i— 1 i— 1 rH i-H i— 1 


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co 


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Trus. 
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CO 


c^i o co co ib 

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+= 


^t -rf* "rfi "^ "^ 


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CD 
CD 


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Oq CO CO CO CO 

y y y y y 

«H 

I— 1 1— 1 I—l T— 1 

II 1 M 

CO CM CM CM CM 


'd 


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00 i— 1 i-h CM CM 


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CO O O O O 
i— 1 i—i i— 1 i— 1 


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CD 

pq 


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CD 

CD 


r:,T73!-i-:*tfx;^-?: -? 
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y y y y y 

t— 1 i— 1 rH i— 1 i— 1 

Mill 

CO COtH -^ ^cH 


T3 


O CO ^ t^ i-i 
CO CO CM OT CO 


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t-H CO CO CO CO 


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o 
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co 


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y y y y y 

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CD 

43 

CO 


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^ - X J^ 1 -* >. X 
rH f— i— i i— 1— 

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CM CM CM CM CO 


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CD 
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30 



III 



TOP REINFORCING E>/\RS 




























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See note on bottom of page 28. 







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per 
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foot 


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O O O O O 


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4H 




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tinds 
3teeL 
per 
quare 
foot 


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CM CM t^ 35 O 


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X X X M X 


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32 



IV 



-TOP REINFORCING BARS 



S?»3Sr ,l r™»!*7sroS? Br ^?3*F^^ 



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Plan. 

Fig. 18. 

Note. — For extra heavy beams place one or two short bars in girder as shown 
in Section "a." 



4) 



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34 



Kahn System of 



Applications of the Kahn Trussed Bar. 

The usages of this bar are so great that it is impossible to illustrate all 
within this pamphlet. Some of the more important adaptations are herewith 
noted : 



Floor Construction. 

The Kahn trussed bar lends itself admirably to various forms of floor 
construction, the most common of which are : 

The reinforced concrete slab. 

The reinforced hollow tile floor. 

Figures 15, 16, 17, 18, represent typical methods of beam arrangement in 
the solid concrete system. 

In selecting from these methods, one should be guided by the length of 
span required, as well as the load per sq. ft. For instance, the method shown 
in Fig. 18 is obviously better adapted to long spans and heavy load than that 
represented by Fig. 17. 

The essential points to be noticed in this system of construction and which 
cannot be obtained by any other system are : 

Continuous This is obtained by the crossing of bars and invert- 

Slab Action ing them over all supports, so that a load placed in any 

panel is distributed in every direction and is carried 
very largely by the adjoining panels through the cantilever action of the 
inverted bars. Thus, if a hole were cut out of the slab, if poor concrete were 
used in any section, or any of the beams utterly destroyed, the floor would 
still possess a certain factor of safety, owing to the cantilever action of the 
inverted bars. 

Rigiditv of When horizontal reinforcement alone is used, it is 

Floor reasonable to say that the amount of sag is proportional 

Construction to the length of the steel bars unsupported; that is, 

the entire length of the bar. In fact, the horizontal reinforcement does 
not come into the tension until beams or slabs have become sagged. With the 
Kahn trussed bar, however, this length is reduced to that portion between the 
two central diagonal members. For this reason, a deflection under dead weight 
alone, which is so common in all other systems, is practically impossible with 
the Kahn trussed bar, where the floor has been properly designed. It is also 
important to note in this construction the resistance offered to vibration. 



Reinforced Concrete 



35 



Positive This also is a very common fault m all other sys- 

prevention . 

agiinst terns. 1 he inverted Kahn bars in top of slab over beams 

cracking of give the continuous action which is an invariable proof 

finished floor against its cracking. The effects of temperature is thus 

over supports 

taken care of at the most vulnerable points. 

Facility of The Kahn trussed bar is the only known reinforcing 

erection b ar - m w hich both the shear and tension members are 

combined in one piece. It is needless to say that the 
saving in cost of erection alone, due to this fact, warrants the exclusive use of 
this bar. There is no need to depend upon the proper placing of innumerable 
small members by careless workmen; no need to risk life and success upon 
the exact mixture of concrete by unskilled laborers. In fact, if by accident, 
frozen or otherwise objectionable concrete is placed in a structure, there still 
remains a factor of safety of at least 2 or 3. We challenge any other method 
of construction to show safety values such as these. The reason for this is 
that the adhesion, grip, tension, or mechanical bond of concrete, are not at all 
depended upon. This bar needs the concrete in compression only, due to arch 
action. 

Failure of a structure when reinforced by the Kahn 
Method of sheared bar, and when tested to destruction, occurs inva- 

riably by the breaking of the steel (See Fig. 34), and 
destruction then only after the steel has stretched about 20 to 25% 

of its entire length. Collapse or sudden failure is abso- 
lutely impossible, as this bar provides positively for shear. The certainty of 
knowledge that a structure cannot fail without the pulling in two of the steel 
at the center, thus making correct calculations possible, is sufficient reason why 
the Kahn sheared bar is being universally adopted as a standard of excellence 
in reinforcing material for concrete. 

Reinforced Hollow Tile Construction. 

Figures 19, 20, 21, represent our method of floor construction, No. 2. It 
is impossible to conceive of a more simple, direct, and beautiful construction 
than this. Its great advantages are as follows : 

The blocks are laid in rows with a 3" or 4" space 
Speed of intervening. Into these spaces is placed an inch of 

cement mortar and the Kahn trussed bar. They are then 
filled with a rather rich concrete. We have thus formed reinforced concrete 
joists, about 16" on centers. The tile serves merely as filling empty spaces, 
the floor weight being carried directly by the intermediate beams. 




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38 



Centering may be removed with exceptional speed, as the concrete is rich 
and is placed in the form of joists instead of as a slab. The dead weight of 
the floor also is very light; in fact, more so than any system in use at the 
present time. Under ordinary conditions centering may be taken out within 
a week. For that reason a building is not delayed, since just about as quickly 
as the mason can lay up the exterior brick walls, the fireproofing contractor 
can remove his centering and replace it ready for the next floor. 

The concrete being placed in the form of vertical joists in place of a flat 
floor slab, gives remarkably great carrying capacity. 

In this system of construction advantage is taken of the lightness of tile, 
together with the strength of reinforced concrete. Their combination makes 
the most perfect fireproof floor known to-day for certain purposes. 

In hospitals, residences, schools, hotels, etc., it is 
auaHties absolutely essential that the floors be made sound proof. 

This result is accomplished in the Kahn re-inforced 
hollow tile construction almost with perfection, as the air spaces in the tile 
form stops for sound and break up transmission. 

Length of These may be built up to 30 feet with the same ease 

s P an of construction as is done for 14 or 16 ft. with the solid 

concrete slab. 

The Trussed Concrete Steel Company constantly builds girders up to 
30 and 40 ft. span in reinforced concrete. With their system of tile construc- 
tion joists of this nature are provided practically every 16". The advantage 
of this system to the Architect in preparing his plans, due to the use of long 
spans, should alone be sufficient reason for its specification. 

Practically all intermediate beams are avoided and plans need call for 
only the necessary supporting walls, and possibly a center line of girders. 
Flat • Individual beams are almost entirely avoided with 

ceilings this system, and in all cases a flat ceiling is provided 

ready for plastering. 

By reason of the fact that the carrying members are 

Rigidity of • r , < // n 

construction reinforced concrete joists 15 or 16 on centers, the 

floor possesses a remarkable rigidity. Deflection under 
safe loading is practically unknown. In fact the Trussed Concrete Steel 
Company agrees to test any of its floors to twice their safe carrying capacity 
without undue deflection. 

Footings. 

See Fig. 22a. The simplest and most economical footing in existence, 
requiring less excavation and concrete than any other method, may be obtained 




Fig. 20. 

Method of laying Kahn System of Reinforced Hollow Tile Construction. Lay tile dry, in rows about 
16" o. c. Then insert one Kahn Trussed Bar in each space between these rows of tile, 

and fill with 1:2:4 concrete. 




Fig. 21. 

Kahn System of Reinforced Hollow Tile Construction. Spans shown above are 16' 0" clear. 

Floor is 6" thick. Note the flat ceiling ready for plaster. 

Dead weight of tile floor construction 36 lbs. per sq. ft. 



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41 



by using the Kahn sheared bar. It is designed on the principle of a cantilever 
beam. The bars are crossed at right angles, thus distributing the upward 
pressure equally in all directions. 

Where there is an upward pressure in a foundation, it is best resisted by 
a slab, reinforced as an inverted floor slab, and securely tied by beams to the 
columns. 

On page 40 appears a table giving dimensions of column footings for 
various conditions. 



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Retaining Walls. 

Retaining walls of the gravity type afford 
excellent use for this bar (See Figs. 23, 
24). This construction is simply a system 
of beams, slabs, and buttresses. (See page 
.. on floor construction). When very 
high walls are desired, it is often very eco- 
nomical to use an intermediate shelf or 
slab, see Fig. 23, which construction re- 
duces the problem to smaller walls, one 
above the other. 

The buttresses illustrate another ad- 
mirable property of this bar, namely, the 
ability to distribute a pull in a large block 
of concrete by means of the sheared up 
members. It is as a result of this princi- 
ciple, only, that the entire mass of concrete 
may be utilized. 

This principle and method may also 
be applied to reservoirs, cisterns, abut- 
ments, etc. 

Gravity Dams. 

Gravity dams, see Fig. 25, offer a method of construction which, if proper 
reinforcement is used, will be more economical, stronger and safer than the 
ordinary method. In this construction all slabs, buttresses, and beams, are 
rigidly connected by inverted reinforcing bars, thus forming, not merely a 
monolithic structure, but a stiff, strong combination of well balanced members. 

The outer shell completely closes the interior with the exception of erec- 
tion openings. Through these, the interior may be filled with stone, gravel, 
earth, or any convenient material, thereby forming a practically indestructible 



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Fie. No. 22a. 



42 




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KAHN ^Y5TEA 

OF RE1NFORCILD CONCRETE 
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45 



and water-tight structure, the strength of which increases with age. Surely 
this is a revival of the grand old Roman method of building, the chief virtue 
of which is durability. 

Similar constructions may be used for reservoirs, locks, etc. 



The field in which the Kahn Trussed Bar may be applied and the variety 
of circumstances that may surround its application are so extensive that this 
pamphlet can only attempt to drop a few hints concerning its use. In the 
majority of cases, however, the simplicity with which the Kahn Trussed Bar 
lends itself to application is so obvious that any engineer or architect may 
use it freely with good results. However, in the more difficult and new prob- 
lems, it would be well to consult the engineers of the Trussed Concrete Steel 
Company, thereby obtaining suggestions and advice that might be of great 
value. Their services will be gladly rendered, free of charge. 

The arch diagram shown on page 49, together with tables, etc., on pages 
48, 49, is an adaptation of Prof. Charles E. Greene's method of calculation 
for parabolic ribs with fixed ends. 

Numerous solutions for concrete steel arches have been deduced, but all 
more or less impractical and doubtful. The method given is adopted on 
account of its simplicity. For further description and information regarding 
this, reference is made to 'Trusses and Arches," part 3, by Prof. Charles E. 
Greene. 

Railroad Work. 

We desire to emphasize to railroad men some of the properties that the 
Kahn Trussed bar possesses, and which are of fundamental importance in the 
design of railroad bridges, culverts, tunnels, etc. The following points will 
impress all conscientious Engineers that the Kahn system of reinforced con- 
crete is the only true, scientific and complete method that is particularly 
adapted to railroad construction. : — 

1. General rigidity. 

2. Great durability, due to permanency of masonry, combined with thor- 
ough protection of steel. 

3. Provision for moving and concentrated loading. 

4. Small initial and maintenance cost. 

5. Speed of erection as material is procurable everywhere. 

G. Safety of construction. A concrete beam reinforced with the Kahn 
Trussed bar will deflect as much as 20" before actual destruction occurs. This 
acts as a great warning factor against overloading. 



46 



Arch. 

One of the most beautiful, simple and effective adaptations of the Kahn 
trussed bar is the arch. The theory of an elastic arch resembles that of a 
beam in so far that the maximum bending moment occurs' where the shear is 
minimum, and maximum shear where bending moment is a minimum. This- 
regulates the number and position of the diagonal members, and thus the 
gross area of section is reserved for places of maximum bending moment. 
The bars need not be joined, as the mere lapping of one or two diagonal 
members is sufficient to develop the full strength of the bar. 

The Kahn sheared bar is the only one which may be placed in the intrados 
without fearing the tendency of the bar to straighten. 

One need but look at the latticed effect, so happily produced here, to be 
strongly impressed as to the many merits of the Kahn sheared bar. At the 
crown of the arch, where there is little filling, the effect of concentrated loads- 
can be cared for by cross bars, which act as distributors over the entire width 
of the arch. 

This method of construction may be applied to bridges, culverts, sewers, 
conduits, tunnels, etc. 

See Figs. 26, 28, 29, 37, 48. 




6 



48 



Kahn System of 





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£^H I + 



Reinforced Concrete 



49 



Method of Calculation and Tables for Parabolic Arches. 
(Fixed at Springing and Continuous over Crown) 



S PAN TO BE DIV I P EP INTO IP EQUAL PANELS 

CENTER LINE OF ARCH RING (PARABOLA) 



Values of "Y" for all intermediate points may 
be computed. 




Example Showing Use of Arch Tables. 

Proposition. — To find maximum bending moment at point "8" for arch of 50 / // span, 
rise = 4 span. 

Assume dead load equivalent to earth load (with horizontal surface) 3 / // deep at 
crown and at 100 lbs. per cubic foot. 

Live load = 300 lbs. per square foot. 

Assume loading to act as concentrated at panel points indicated. 
Solution.— The loadings for max. moments at point "8" are (see table) : 

For max. 4- moment = dead load on all points + live load on 7, 8 and 9. 
For max. — moment = dead load on all points + live load 1, 2, 3, 4, 5 and 6. 

Loading for max. horizontal thrust is dead and live loads on all points. 



Point. 


Max. 


4- Moment at "8" 


Max 


. — Moment 

at "8" 


Max. 


Horizontal Thrust. 








M=m c W 




M=m c W 










9 


"m" 

from table. 

+ .028 


c 


W 




W 




"H" 

See table 


c 

k 


W 


H=hcW 

~ k 


+ 


— 


+ 


25 


5300 


3700 


3800 


2700 


.061 


3.5 


5300 


1130 


8 


+ .107 


25 


4300 


11500 




2800 


7500 


.192 


3.5 


4300 


2890 


7 


+ • 028 


25 


SHOO 


2500 




2100 


1500 


.331 


3 5 


3600 


4180 


6 


— .017 


25 


1H50 




700 


3150 


1350 


.432 


3.5 


3150 


4760 


5 


-.037 


25 


1500 




1400 


3000 




2800 


.469 


S.5 


3000 


4920 


4 


-.040 


25 


1650 




1650 


3150 




3150 


.432 


3.5 


3150 


4760 


3 


-.031 


25 


2100 




1600 


3600 




2800 


.331 


3.5 


3600 


4180 


2 


-.017 


25 


2800 




1200 


4300 




1850 


.192 


3.5 


4300 


2890 


J 


-.005 
Total, 


25 


3800 




500 


5300 


700 


.061 


3.5 


5300 


1130 






17700 


7050 




11700 12650 








30840 



Max. 4- moment = 17700 - 7050 = + 10650 ft. lbs. 
Max. — moment = 11700 - 12650 = — 950 ft. lbs. 



50 



Kahn System of 







" "^^/^7Z /r Hafm~E><3irS~^o7iJ'inuoJsio"o.c. Extrodos 



>/z*l\' Kahn Bars IZ'o.c. Exfrodos. 



/ntrodos. 



fc \.->/4"*r 



Z'oac-A 



ZSi. 



P-^l 



j; Stf ufKahn &ars continuous JZ'b-c. /nfrodosS f ST 



-CVMEhALP PLA/NI orUPPCRARCh— O/MtHALr PLAA1 Of LOWER ARCJ1~ 



luluIuliJ 



4' 5' 6' 



-scale y^i/Ycn- irooT- 

«-KAttA 5T5TEM Or REI/M FORCED COAICRLTE 
APPLIED TO A TWEAJTY TOOT StWER^ 
TttE. TRUSSED CO/\|CRETC.-STCCL COMPAAJY, 
UA1IO/N TRUST BUILDIAJG- -DETROIT 



Fig. 28. 



Reinforced Concrete 



51 




_BJ 



~/1ALP SEXTIO/N W/TH HAPLD 
BOTTOM &6IDE5 TO 5PPJ/NGWG 



-HALF SECTIO/V WITMvSOrT 
50TTOM & 3IDE5 TO SP£|/NGI/VG~* 




-O/ME. MAi_r v5&CTIO/V A-B 



?' 



3' 



~OAIE MALP" Pi-A/M- 

I ' O " 

li-i 1 1 1 1 iTTTTI 

KAHAI 5YSTEM Or R,£l/\irORCED CO/MCR.E.TE 
APPLIED TO ^EVVEk CO/VaTR.UCTIOAI- 
THE TR.U55ED COAlCR.ET£-5TLEL COMPAAIIO 
- UA1IO/N TR.05T BUILDING- ~ DETROIT- 

Fig. 29. 



52 



Kahn System of 



CROSS BAR TO RE5I5T LFFLCT5 
OF Tt^PtRATURE A.ND SHRINKAGE,. 



INVERTED BARS A&SURIN6 

— CONTINUOUS ACTION 

AND GF.JS£.RA1_ RIGIDITY. 



Plan showing Arranglaent orBARs. 



3332H2!r: 



\"^V N N 



///: , S;-\\^..\- 



•////■/j;\;VN\ 



TOP RE.INFOBCING .BARS. 

Lb j^ 

FT. O O Fl J-IME. 



top KtirNFoRCirsis Bar 



^^ m^v - 4 'tilK4aiHHHHJRF S^ 




IB JK Tij-b. 

1 I 

i i i i 

Kahn ~1d y^t^e^^v^ or- 

„ , __ REJNFORCELD CONCRETE. 

Typical Construction belt- I _B. 



4=11 



Fig. 30. 



Reinforced Concrete 



53 



Tables 



General 
Description 



In these tables it is assumed that floors have been con- 
structed in accordance with the Kahn System of Reinforce- 
ment, as illustrated in our catalogue, and that bars have 
been inverted in their position over supports to procure the effects of continu- 
ous beam action. 

2. Concrete to be composed of the best grade of Portland Cement, sharp, 
clean sand and broken stone or gravel, in the proportions of 1 :2 z /2 :5 for floor 
slabs, and 1 :2 :4 for beams. Broken stone or gravel al" ring. 

3. Bars to be placed at least Y\" from the bottom of the beam, and the 
concrete thoroughly rammed in place. 

4. Centering not to be removed in less than two and one-half weeks, if the 
concrete has not been subjected to frost. If freezing has occurred, centering 
must not be removed until every indication of frost is removed, and the con- 
crete thoroughly set. 

Tables were calculated for a factor of safety of 4. However, when this 
system is incorporated into a combination of continuous beams, the resultant 
factor of safety rises to 6 or 7. This is clue to arch action, tension in concrete, 
continuity, and slab action, as well as numerous other facts which, on account 
of the difficulty attending their exact calculation, it is deemed advisable to 
neglect in these tables. 



The following are the usual assumptions made in practice for super- 
imposed loads : 

Floors of dwellings and offices 70 lbs. per sq. ft. 

Floors of churches, theaters, and ball rooms 250 

Floors of warehouses 200 to 250 

Floors for heavy machinery 250 to 400 



54 



Kahn System of 



Bending moments of Beams under various Systems 

of Loading 



W=total load. 



l=length of beam. 



(1) Beam fixed at one end and loaded 
at the other. 




i) 



\ww \~^\ 



Safe load=^ that given in tables, pages 
36 and 37. 

Maximum bending moment at point of sup- 
port=Wl. 

Maximum shear at point of support=W. 



(2) Beam fixed at one end and uniformly 



loaded. 



id oooooooocb 




\\\\\\\\\ 



Safe load=^4 that given in tables, pages 
36 and 37. 

Maximum bending moment at point of sup- 
port^ Wl. 

Maximum shear at point of support=W. 



(3) Beam supported at both ends, single 
load in the middle. 



a 



\\\ /// 



"r c 

Safe load=>2 that given in tables, pages 
36 and 37. 

Maximum bending moment at middle of 
beam=^ Wl. 

Maximum shear at points of support= ^2 W. 



(4) Beams supported at both ends and 
uniformly loaded. 

crrrrrrmp 



*% 



Safe load=that given in tables, pages 36 
and 37. 

Maximum bending moment at middle of 
beam=^ Wl. 

Maximum shear at points of suppor't=^ W. 



(5) Continuous beam supported at three points and uniformly loaded. 



WW / 



\ / 



w 



I 



Safe load=that given in tables, pages 36 and 37. 
Maximum bending moment at center pier— ^$ Wl. 
Maximum shear at center support=^ W. 



(6) Continuous beam supported at four points and uniformly loaded. 

.ooooooonoorrrrTTr YyYYTTTyYYYTYT) 

r^ ii 



Safe load= f that given in tables, pages 36 and 37. 
Maximum bending moment at interior piers=-iV Wl. 
Maximum shear= T % W. 



Reinforced Concrete 



55 



Formulae To locate the neutral axis of a reinforced concrete 

f beam, it is supposed that the same is an elastic structure, 

Reinforced in which both materials yield under a strain in the in- 

Concrete verse ratio of their modular of elasticity. Since the 

modulus for steel is about 30,000,000, and that of con- 
crete 2,000,000, their ratio is approximately fifteen, and a beam would deflect 
in the same manner if the steel were replaced by a strip of concrete of equal 
depth, but with an area fifteen times as great. For such a beam the neutral, axis 
would correspond to the center of gravity of the increased section. Having 
established the neutral axis, the total moment of resistance equals the com- 
bined moment of the steel in tension and the concrete in comparison, about 
the neutral axis. 



i 



» 



% 



Oreo of Compression 
Jieu+ro/ J?x/s 



E s =modulus of elasticity of steel = 30,000,000. 
E c =modulus of elasticity of concrete=2,ooo,ooo. 
F ^ultimate tensile strength of steel=64,ooo. 
f t=ultimate tensile strength of concrete=200. 
f d=ultimate compressive strength of concrete 

=3,000. 
a =area of metal. 
i 5 a+bd2 



30a-f-2bd 



f by 2 
t 



Ultimate bending moment=:Moment of Resistances \ ^(d-y)4-y > aF-j- 

If tensile strength of concrete is disregarded, 

Ultimate B.M.=M.R= j#(d-y)+y} aF. 

For safe loading, assume one-fourth or one-fifth of above values. 
Note — Breadth of beam=b, should never be less than aF. 

1800 (d-y) 

Where a floor slab rests upon a beam and forms a part of it, it seems en- 
tirely reasonable to assume that the lever arm for the moment of resistance is 
equal to the distance between the center of gravity of the metal and the center 
of the floor slab. In such cases, the steel reinforcement in the slab should be 
reversed over the place of support to take care of the negative bending moment 
existing there. In the tables given for floor slabs, it has been assumed that the 
bending moment has been reduced from 1-8 Wl to 1-10 AVI, and results are 
thus proportioned. 

c . Carrying capacity where length of column does not ex- 

Formulae ceed fifteen times the least diameter. 

Safe load=4oo(A c -l-i5As). Ac =area of concrete. As =area of steel reinforcement. 

In this construction it is absolutely essential that the prongs are bent at 45° with the main 
member, that they extend entirely across the column, and that the concrete is tamped in 
sections not exceeding 12 inches to insure absence of voids. 



56 



Kahn System of 



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<!WP5m 



Reinforced Concrete 



57 






m 



(ft 

<d 

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d 

3 

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01 



Examples 
showing the 
use of Tables 



Let it be required to construct a floor panel 15 ft. x IS ft.. 

to carry a total live load of 125 lbs. per square foot. It 

will be best to have the floor bars extend across the 

shorter spans 15 feet. Refer to tables on spacing of bars. 

using ^"xl^" bars. For a 6" floor slab, these bars 

should be spaced 11 inches on centres; for a 5" floor slab, Sy 2 inches on 

centres. Or the heavier bars %"x2*/4" may be used, spaced 18^4 inches on 

centres, with 5" thickness of floor slab. 

The main carrying beams will be those of 18 feet span. The load thereon 
will be 18xl5xl25=33.7501bs.=337.5 cwt, plus the dead load of the floor 
slab (since the dead load of the floor slab becomes the live load on the beam) 
This dead load being assumed at 140 lbs. per cu. ft. By referring to the tables 
on safe live loads for beams, a beam carrying this load can quickly be found. 



62 



Kahn System of 



Specifications for Reinforced 
Concrete 



The work called for under these specifications, consists of 



It is desired to have the work executed entirely in reinforced concrete, 
without the use of steel beams in any way. 

No system of construction will be considered that does not provide for 
shearing stresses at the ends of girders and beams. 

All floors will be made sufficiently strong to carry their own weight, and 

a superimposed load of lbs. Ceilings to carry 

lbs., roof lbs. The load per sq. ft. will include whatever floor 

finish is used on top of concrete construction. 

Right is reserved to test any unit area of the floor construction to failure. 
If it fails under a superimposed load of less than four times the above amounts 
per sq. ft. for the respective floors, over the entire area tested, the damage must 
be made good, and all work must be strengthened so as to meet the require- 
ments of these specifications, without expense to the owner. 

Wherever spans exceed 16 ft., reinforced concrete beams shall be used. 
These must be in accordance with an approved system of construction, and must 
provide, not only for bending moment, but also* for shear, by being reinforced 
in the vertical plane as well as in the horizontal. These shear members must 
make an angle with the horizontal member, preferably 45 degrees, and must be 
rigidly connected to the main horizontal tension bar, similarly to the Kahn 
system. The adhesion of concrete to steel, in providing for shear, will not be 
assumed at more than 50 lbs. per sq. in. Vertical reinforcement must, there- 
fore, be sufficiently strong to provide for the internal strains for which con- 
crete is not calculated. 

The reinforcing metal must be protected from fire by at least one inch of 
concrete, measured from the lower surface of the slab to the nearest point of 
the metal. The metal in girders and beams must be protected by a minimum 
thickness of l 1 /*" of concrete. 

All concrete must be composed of an approved quality of Portland cement, 
sand, and broken stone, or gravel. If gravel is used, it must be clean and vary 



Reinforced Concrete 



63 



in size from that of a pea to one inch. The broken stone must be free from fine 
dust, and broken to pass a 1" screen. 

The concrete for floor slabs must be of a proportion as 1 '2y 2 :5, of cement, 
sand, and broken stone. For beams, 1 :2 :4. 

Concrete shall generally be placed in the work in layers not exceeding six 
inches in thickness, and, in general, one layer shall be entirely completed before 
another is commenced. If delivered by wheel barrows, it shall be dumped as 
closely as possible to where it is needed, in order to avoid re-handling or ex- 
cavating while in the mold. Each layer must be thoroughly rammed until the 
moisture comes to the surface. 

All concrete to be mixed by one of the approved standard batch machine 
mixers. The resultant mixture of sand, cement, and stone, to be as nearly as 
possible uniform in character, mortar being equally distributed throughout the 
mass of stone. 

The mixture shall be made of such consistency, that when thoroughly 
rammed, it will quake slightly; but it shall not, in general, be thin enough to 
quake in the barrow or before ramming. In order that girder or beam molds 
be well filled, mix the concrete into a more plastic state. 

Each bidder must submit general sketches showing his system of re- 
inforced concrete, and the method proposed for applying it to the work in 
hand, the general location of beams, thickness of floor slabs, etc. He must state 
what is the quality of his steel bars as to tensile strength, elastic limit, elonga- 
tion, etc. In no case must the steel be inferior to the standard structural 
material with an ultimate strength of from 55,000 to 60,000 lbs. per square 
inch, as recently adopted by the Association of Steel Manufacturers. 

The successful bidder will be required to furnish detail working drawings, 
and specifications, which must be approved by the architect before work is 
commenced. The centering must be strong enough to hold the plastic concrete 
true to line, level, and shape. 

If at any time during the progress of the work, any concrete is improperly 
mixed or proportioned, the architect shall have the power to condemn it at 
once, and prevent its incorporation in the work. 

Concrete work will be suspended whenever, in the judgment of the archi- 
tect, it is liable to injury from freezing. 

Steel bars for use in the concrete will not be painted. A slight film of red 
rust will not be objectionable, but any bar on which rust scales have begun to 
form will be rejected. 

No bid will be considered, except from persons or firms with recent and 
extensive experience in the form of work called for. 







Fig. 31 




Fig. 32. 




Fig. 33. 



Test of Kahn Reinforced Hollow Tile 

Construction 

This floor was constructed in accordance with the Kahn System of Rein- 
forced Hollow Tile Construction. Reinforcement 34 -inch Kahn Trussed 
Bars, with 8-inch standard diagonals; reinforced concrete beams between tiles, 
4x8 inches; dimensions of floor slab given in sketch. 

Mixture of concrete, cement, sand, and crushed stone, proportioned 1 ; 2 ; 
5, mixed by hand and five weeks old. 

Floor was loaded with bars of nut iron, 3 inches wide, 2*4 inches thick, 
11 feet to 15 feet long; the weight of each bar ranged from 200 to 300 lbs.; 
each bar was weighed before putting on the slab; the load was uniformly 
distributed. 

The record of the weights and deflections taken were as follows : 

36,320 lbs. Vie in. deflection. 41,500 lbs. % in. deflection. 
37,850 " % " " 43,130 " % " 

40,410 " % e " 

A small hair-like crack appeared l^feet off center of the floor slab when 
a load of 44,599 pounds was applied. A deflection of y 2 inch showed up im- 
mediately after. 

The deflection gradually increased as the load was applied. At 48,355 
pounds a similar crack appeared iy 2 feet on the opposite side of the center line. 
These were the only cracks in evidence until 53,345 pounds were applied. 



12,395 lbs. 


No deflection 


27,470 " 


tt ( i 


31,510 " 


%2 in " 



66 



From this time on, deflections increased more rapidly. Cracks appeared after 
this at about 4 inch intervals throughout the center of the beam. Each crack 
would open 3/16 inch to y 2 inch, and then another crack would appear. All 
the cracks were in straight lines and at right angles with the bottom of the slab. 
All cracks Avere within the middle five feet of the beams; no cracks whatever 
were beyond this on either side. 

The failure was a slow, gradual failure, after the elastic limit of the steel 
was surpassed, the steel then stretching in the middle five feet and gradually 
letting clown the beam, until a deflection of 20 inches was reached, its center 
touching the ground. The dead weight of the floor was 5,400 pounds. The 
total deflection when loading was stopped, was 20 inches. The concrete did 
not crush, but opened up at the bottom. 

The total live load over 90 sq. ft. of floor slab, was 60,000 pounds. 
Dead weight 5,400 

Total in all 65,400 

Equivalent to a load of 730 " per sq. ft. 

Safe Load . 100 " " 

Factor of Safety 7.3 



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70 



Kahn System of 






__i L___4frL 




£ 4-' 6' 8' /o' . 

scale '/a'lncn- i Poor. > ' Kl^AAL KL-Aa/N 

~5ttOWI/\|G KAM^ R.CI/N FORCED CONCRETE APPLIED TO fLOOR. CO/NSTRUCTIO/N Of 

BUILDI/NGD.~ 

'"Girder Decrferrlrrq./sfeepers, /6*a.c.-^ \ I 7bp Z, 4"x4"xJ£\ j ^Hf-g^r^tew 




PLA/S OP COLUMN FOOTING. 



COLUMAI POOTI/NG 



Fig. 38. 



Reinforced Concrete 



71 



^^ 



i5ca./e 



/FooT^ 



^H 




--—i r:z ~ ~~~zz^jL'z.~—z _; > 

^r^fa^y^T^.^- — - - ~n f 1 -~- r ~-^"— - -J r- — — — ~^ 
rz zJir_r_ zrz n" pfe-T* &&hE£&*-' ! ~^ 



-Tg*igfiahn Sin, .;' 






J-L 



'S r- /' ^" ..^SnS 



2^ 



,-va;<}' 



M PLAAI OFCOVCR 5LAD 

gggfea^fofe ~2 x {£/teh0 Sheared 3ars. 8oc 



'/Or/? "Concrete 3eam'o 
x-Z'Hahn Bars. 



mmwm^wwmmmmm^mmMmmmmmmmii^ 



k x /^" /&p Reinforcing 3ar 



J texfjr" Kahn Sheared Bars. 

JH' [from 8" tofZ"ao. 
I 
J= ;. £ H|- 2 ^ ftahn Sheared Bars /8 o-c 

I J [(?)%"x2"Kahn 5heared Bats 
l\l n e&- Buttress 



NOTE-' Finished Cement Coat, 

on Side Walls, Posts, and Bottom 

fo be of- Port /and 1; Sandlr i"Thich 




PLAN OF FOOTING 
OF COLUMN 5. 



t- \i" X/ 'i' 7°P Reinforcing Bars 
\ \pl Corer 5lab.-2'rfeoch Baiy 

^>\z" xl £" T op Reinforcinq Bar 
^\in '?" Beam. J 

io\?o" Concrete 6irder 
3"*?"Hahn 3arj 

10"* IO" Concrete Pasts 
(4->2 * /fKahn 5a r 5 

DRAWING 5M0WI/NG 
KAtt/^ RD/VirORCCD 
CO/MCRETE 5YSTEM 
APPLIED TO COVERED 
RESERVOIR COAl = 
STRUCTIO/Y 



B H}|)'>' '-' :, ;'i i'xli" Kahn Ban 
i i < i tin ■'■ i in Column Footir, 



-~ -^y^m ' ■ ^ii^mv\^iiMi/Mw^iyM^(\^(M '" Co ' an '" Fooi "J 



continuous throughout YYaU Fooling. 



\ \[(o)Kah'n Sheared dars. OPPTI^AI A~T«A D> \£'* f £ f r*% r 9?' 

■ l \///xlf in Buttress SECTIO/n ATA"B- X.'" Col. Roof ^ 



rs 

7 



Fig. 39. 



72 



Kahn System of 



KAHN TRUSSED 
LINTEL 




PATEN TEJ 



Fig. 40. 



Figures 40, 41 and 42 show general views of the Kahn Trussed Lintels. 
The advantages of a flat headed opening are very great as compared with a 
segmentally arched opening, and when the brick work above is properly sup- 
ported, wall cracks are entirely avoided. This type of lintel construction must 
appeal to the architect at once. No steel beams, channels, or other carrying 
members whatever, are employed ; the very strength of the wall itself is made 
use of to carry its own weight. Tests which we have made on lintels of this 
type, have developed strengths greater than steel I beams of the same depth. 



Reinforced Concrete 



^ 



x \ 




A- 



Ejlevatiom, "LiNTEuTYpe A 



Fig. 41 



-CONCESV5 



sisex. fx-^te 



SECTION. AcA ■ 




El,ev^o-ion • Section • 

Ljntex,TVpe G 





SExmoNcc 



Fig. 42. 



74 



Kahn System of 



^ Fr T ' r T , r ^ 




**#'i-j<. 



Fig. 43. 




Fig. 44. 

Kahn Trussed Lintel, 12 in. deep, 13 in. wide, 12 ft. span, 
Load, steel billets, 40720 lbs. Deflection % in. 



Reinforced Concrete 



75 




Fig. 45. 



Figures 43, 44 and 45 show some tests which were made on lintels as 
above described. The load, which is herewith illustrated, is far in excess of 
that which could possibly come in actual construction, as the tendency of a 
wall is to arch itself above an opening, and the actual weight which rests upon 
a lintel is that of a triangle of masonry, forming angles of about 60 degrees 
with the top of the opening. 

The Trussed Concrete Steel Company has always at hand a competent 
corps of engineers who will be very glad to deal with any special problems 
which the architect may have at hand, and their services will gladly be given, 
free of charge, for any construction wherein it is desired to use this type of 
reinforcement. 



Test of Beams Reinforced with Kahn Trussed Bars 




Jpa/? Po-o" £# Tr^se^^arj 



Fig. 46. 




Fig. 47. 
Depth of beam=20 / 



Amounts of Cement, Sand and Stone required for 
concrete mixtures of various proportions 





Concrete with 2% inch Stone 




Concrete v 


fith Gravel % inch and under 


Proportons 
Mixture 


of 


Required for 1 cubic yard 


Proportions of 
Mixture 


Require 


d for 1 cubic yard 


Ce- 
ment 


'Sand 


Stone 


Cement, 
Bbls. 


Sand, 
c. yds. 


Stone, 
c. yds. 


Ce- 
ment 


Sand 


Gravel 

2.5 


Cement, 
Bbls. 

2.10 


Sand, 
c yds. 


Gravel, 
c. yds 


1 


1 


2 


2.72 


0.41 


0.83 


1 


1 


0.32 


0.80 


1 


1 


2.5 


2.41 


0.37 


0.92 


1 


1 


3.0 


1.89 


0.29 


0.86 


1 


1 


3.0 


2.16 


0.33 


0.98 


1 


1 


3.5 


1.71 


0.26 


0.91 














1 
1 


1 


4.0 


1.55 


0.24 


0.94 


1 


1.5 


2.5 


2.16 


0.49 


0.82 


1.5 


3.0 


1.71 


0.39 


0.78 


1 


1.5 


3.0 


1.96 


0.45 


0.89 


1 


1.5 


3.5 


1.57 


0.36 


0.83 


1 


1.5 


3.5 


1.79 


0.41 


0.96 


1 


1.5 


4.0 


1.46 


0.33 


0.88 


1 


1.5 


4.0 


1.64 


0.38 


1.00 


1 


1.5 


4.5 


1.34 


0.31 


0.91 














1 
1 


1.5 


5.0 


1.24 


0.28 
0.44 


0.94 


1 


2.0 


3.0 


1.78 


0.54 


0.81 


2.0 


3.5 


1.44 


0.77 


] 


2.0 


3.5 


1.66 


0.50 


0.88 


1 


2 


4.0 


1.34 


0.41 


0.81 


1 


2.0 


4.0 


1.53 


0.47 


0.93 


1 


2.0 


4.5 


1.26 


0.38 


0.86 


1 


2.0 


4.5 


1.43 


0.43 


0.98 


1 


2.0 


5.0 


1.17 


0.36 


0.89 














1 


2.0 


6.0 
4.0 


1.03 
1.24 


0.31 


0.94 


1 


2.5 


3.5 


1.51 


0.58 


0.81 


1 


2.5 


0.47 


0.75 


1 


2.5 


4.0 


1.42 


0.54 


0.87 


1 


2.5 


4.5 


1.16 


0.44 


0.80 


1 


2.5 


4.5 


1.33 


0.51 


0.91 


1 


2.5 


5.0 


1.10 


0.42 


0.83 


1 


2.5 


5.0 


1.26 


0.48 


0.96 


1 


2.5 


5.5 


1.03 


0.39 


0.86 


1 


2.5 


5.5 


1.18 


0.44 


0.99 


1 


2 5 


6.0 


0.98 


0.37 


0.89 














1 


2.5 


7.0 


0.88 
1.03 


0.33 
0.47 


0.93 


1 


3.0 


4.0 


1.32 


0.60 


0.80 


1 


3.0 


5.0 


0.78 


1 


3.0 


4.5 


1.24 


0.57 


0.85 


1 


3.0 


5.5 


0.97 


0.44 


0.8L 


1 


3.0 


5.0 


1.17 


0.54 


0.89 


1 


«.0 


6.0 


0.92 


0.42 


0.84 


1 


3.0 


5.5 


1.11 


0.51 


0.93 


1 


3.0 


6.5 


0.88 


0.40 


0.87 


1 


3.0 


6.0 


1.06 


0.48 


0.97 


1 


3.0 


7.0 


0.84 


0.38 


0.89 














1 


3.0 


7.5 


0.80 


0.37 


0.91 














1 


3.0 
3.5 


8.0 


0.76 
0.88 


0.35 
0.46 


0.93 


1 


3.5 


5.0 


1.11 


0.59 


0.85 


1 


6.0 


0.80 


1 


3.5 


5.5 


1.06 


0.56 


0.89 


1 


3.5 


6.5 


0.83 


0.44 


0.82 


1 


3.5 


6.0 


1.00 


0.53 


0.92 


1 


3.5 


7.0 


0.80 


0.43 


0.85 


1 


3.5 


6.5 


0.96 


0.51 


0.95 


1 


3.5 


7.5 


0.76 


0.41 


0.87 


1 


3.5 


7.0 


0.91 


0.49 


0.98 


1 


3.5 


8.0 


73 


0.39 


0.89 














1 


3.5 


8.5 


0.71 


0.38 


0.91 




4.5 








0.87" 


1 


3.5 
4.0 


9.0 


0.68 


0.36 
0.47 


0.92 


1 


6.0 


0.95 


0.58 


1 


7.0 


0.77 


0.81 


1 


5.0 


6.5 


0.91 


0.55 


0.90 


1 


4.0 


7.5 


0.73 


0.44 


0.83 


1 


4.0 


7.0 


0.87 


0.53 


0.93 


1 


4.0 


8.0 


0.71 


0.43 


0.86 


1 


4.0 


7.5 


0.84 


0.51 


0.96 


1 


4.0 


8.5 


0.68 


0.42 


0.88 


1 


4.0 


8.0 


0.81 


0.49 


0.98 


1 


4.0 


9.0 


0.65 


0.40 


0.89 














1 


4.0 


9.5 


0.63 


0.38 


0.91 










0.57 




1 


4.0 


10.0 

10.0 


0.61 
0.57 


0.37 
0.43 


0.93 


1 


5.5 


8.0 


0.74 


0.91 


1 


5.0 


0.87 


1 


5.0 


9.0 


0.70 


0.53 


0.96 


1 


5.0 


12.0 
12.0 


0.51 


0.38 


0.92 


1 


6.0 


9.0 


0.65 


0.59 


0.89 


1 


6.0 


0.48 


0.44 


0.88 


1 


6.0 
7.0 


10.0 


0.62 


0.56 


0.93 
0.91 


1 


6.0 


14.0 
14.0 


0.43 
0.42 


0.40 


0.92 


1 


11.0 


0.54 


0.51 


1 


7.0 


0.44 


0.88 


1 


7.0 


12.0 


0.52 


0.55 


0.95 


1 


7.0 


16.0 


0.38 


0.40 


0.92 



L.ofC, 



78 



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JUN 20 1904 



115 93 





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INDIANA 46962 











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